Question

Which are characteristics of the graph of the parent absolute value function?

The graph is symmetric with respect to the y-axis.
The two halves of the graph make 45° angles with the x-axis.
The graph is symmetric with respect to the x-axis.
...
The graph is a "V" with vertex at the point (0,0).
The two halves of the graph make 30° angles with the x-axis.

Answer 1

Explanation:

the first, second and fourth statements are correct.

the parent absolute value function is

y = |x|

so, y = x is the foundation. so, the graph is a line that goes exactly diagonally (at 45°) from (0, 0) to infinity.

the special thing about the absolute value is that it delivers only the positive value of whatever is inside the function. so it turns the negative diagonal of y = x up above the x-axis.

and so it makes a perfect "V" sign with the vertex at (0, 0), and it is therefore symmetric around the y-axis (the y-axis is like a mirror).